An electrical grid comprises a multiplicity of nodes, which are connected to one another via electrical lines and which feed electrical power into the electrical grid or draw electrical power from the electrical grid. For stable operation of an electrical grid, in this case quick balancing between fed electrical power and drawn electrical power is required. For this purpose, proportional controllers which set the fed or drawn power depending on the difference between the frequency of the voltage in the respective node and the rated frequency of the electrical grid are used in corresponding nodes. For stable operation of the electrical grid, in this case a proportionality factor and a reference power suitable for the respective proportional controller need to be established. Usually, heuristic approaches for establishing these parameters are used. Then, the grid is analyzed on the basis of complex simulations for stability and robustness and possibly the parameters are re-established.
In document [1], the stability of an electrical grid is investigated taking into consideration the parameters of proportional controllers without there being any description of how the parameters can be set optimally in relation to the stability of the electrical grid. Instead, a fixed ratio between the proportionality factor and the reference power for all generating units in the electrical grid is proposed.
Document [2] describes how the primary control power in an electrical grid can be distributed optimally between the nodes. The primary control power of each node is directly dependent on the proportionality factors of the nodes. For this optimization, the stability reserve of the electrical grid is estimated on the basis of neural networks. In this method, the stability represents a secondary condition and is not used for optimization of the electrical grid.